The group said it had a “well-developed succession process”, which will now be put into action.
The announcement came as Direct Line reported a 13.9 per cent fall in pre-tax profits to £293.8m for the first six months of 2018.
It took a £75m hit in costs for large weather claims after the Beast from the East freezing temperatures, up from just £9m a year ago.
Mr Geddes steered the company through its split from the Royal Bank of Scotland and its London Stock Exchange listing, turning it into a blue-chip stock.
Chairman Mike Biggs said: “We have a well-developed succession process which we will now deploy with the objective of ensuring that we have an excellent successor in place by the time Paul leaves next year.”
Direct Line, whose brands include Churchill, Green Flag and Privilege, said operating profit was £303.1m for the six months ended June, compared with £359.7m a year earlier.
Analysts were expecting an operating profit of £245m, according to company compiled consensus from 15 analysts.